Finite element analysis of dry and wet butt and lap joints AE Bond

MTS Project 3: Environmental Durability of Adhesive Bonds
Report No 12
Finite element analysis of dry and wet butt and lap joints
AE Bond, GC Eckold, CM Jones
GD Jones
April 1996
MEA
AEA Technology plc
424 Harwell, Didcot
Oxfordshire OX1 1 ORA
United Kmgdom
Telephone 01235 821111
Customer Ref:
Document Ref:
File No:
AH 913
AEAT29570/
Facsimile 01235 432481
Document Series:
REPORT
Title:
Report 12
Finite element analysis of dry and wet butt and lap joints
ISSUE RECORD
Issue
Date
1
April 1996
Author
G C Eckold
A E Bond
G D Jones
C M Jones
Checked By
A E Bond
Approved By
G C Eckold
Summary
This report describes a series of finite element analyses performed to assess the sensitivity of lap
and butt joints to variations in geometry and material properties and to attempt to explain
experimental results obtained from a series of durability tests.
In the sensitivity study, for the lap joint it has been found that
specimen gauge length has no effect
mode of loading has no effect
the bond angle has a large effect, with a 14% reduction in strength for a 2’ angle
the effect of adhesive modulus is indeterminate
the adherend yield stress is critical to the mode of failure
For the butt joint, there were fewer parameters to vary. It was found that
the bond angle has little effect
bending moment due to an of&et load reduces the strength by 10% for an extreme angle.
The conclusion is that there is much more variation in the results in the lap joints compared
with the butt joints which is consistent with experimental observation.
The prediction ofjoint strength with ageing was partially successful. For joints with grit blast
surface treatment, where the failure mode is largely interfacial, the butt joint strengths can be
predicted well and the lap joint strengths can be predicted after the initial fall and recovery in
strength. For joints with a grit blast and silane surface treatment, where the failure is largely
cohesive, there was no correlation.
Contents
1. Introduction
3
2 . Finite element models
3
3
4
2.1 LAP JOINT
2.2 BUTT TENSION JOINT
5
3 . Sensitivity Study
3.1 INTRODUCTION
3.2 LAP JOINTS
3.2.1 Effect of Gauge Length
3.2.2 Application of Load
3.2.3 Effect of Bond Angle
3.2.4 Effect of skew
3.2.5 Effect of Adhesive Modulus
3.2.6 Yielding of the adherend
3.3 BUTT JOINTS
3.3.1 Effect of Bond Angle
3.3.2 Applied Bending Moment
3.4 CONCLUSIONS
5
5
5
6
6
6
7
7
7
7
9
9
12
4. Durability
12
12
13
13
13
15
17
17
17
17
4.1
4.2
4.3
4.4
INTRODUCTION
ADHESIVE
FINITE ELEMENT MODEL
RESULTS
4.4.1 Butt Joints
4.4.2 Lap Joints
4.5 DISCUSSION
4.5.1 Butt joints
4.5.2 Lap joints
4.6 CONCLUSIONS
5. Acknowledgements
18
6. References
19
7. Table of figures
20
2
1 m Introduction
As part of MTS 3 Task 2l, a large number ofjoints underwent a durability testing programme.
The range ofjoint configurations and adhesive/adherend/surface treatments used were
numerable. In addition, several ageing conditions were considered, although the main ageing
condition used was water immersion at 6OOC. The aim of this study was to use finite element
analysis to try to gain an insight into the observations made from the durability results. Areas of
interest include the sensitivity of the results due to small changes in test conditions, why some
joints are better at distinguishing between surface pre-treatments, and what effect water ingress
has on the stress distributions.
The joints considered in this study were limited to the lap shear and butt tension joints.
2m Finite element models
The proprietary finite element codes used for these analyses was ABAQUS version 5.4 and
version 5.5.
2.1 LAP JOINT
The standard lap joint considered here was :
l
Adherend:
Mild steel
l
Adhesive:
Araldite 2007
l
Width:
2omm
l
Overlap:
1omm
l
Adherend thickness:
1.2 mm
l
Adhesive thickness:
0.25 mm
l
Distance between clamps: 70 mm
l
Fillet:
none
l
Failure load
5.24 kN1
The other lap joints modelled included minor variations on this theme to enable particular
aspects of the joint to be considered. The lap joint was modelled in two dimensional cross
section using plain strain, second order, reduced integration elements (CPE8R) throughout. It
has been shown2 that these elements accurately represent the condition at the centre of the joint
where the peel stresses are at their greatest. As lap joints are generally wide in relation to the
overlap length, edge effects are minimal and thus it was not felt that three dimensional
modelling of the joint was appropriate.
A fine mesh of 4 elements deep (Figure 1) was used to enable through thickness stresses in the
adhesive to be assessed with reasonable accuracy. A fairly fine mesh was required in the
3
I
adherend either side of the overlap, as this is where bending (and yielding) of the adherend
occurs. A coarse mesh here results in a poor stress distribution. Further away from the overlap,
a coarser mesh was used for the adhere&s as the loading there is primarily axial and uniform.
Boundary conditions were applied to the mesh, so that the left hand end of the joint is encastre.
A concentrated load was applied to the right hand end. A multi-point constraint was used so
that the whole of the right hand end moves together in the axial direction without producing a
stress concentration that would cause local yielding of the adherend.
The adhesive investigated in this report is Araldite 2007 (sometimes known by its former
designation AV119), which is a hot cure one part epoxy, manufactured by Ciba Polymers Ltd.
Non-linear properties were used for both the adhesive and the adherend. Araldite 2007 is
highly non-linear and only has a small linear elastic region on its stress-strain curve (Figure 2).
Local yielding of the adherend occurs where it bends, so the non-linear properties of steel were
required to model this correctly. The non-linear geometry option was also used, as large
displacements occur.
As the overlap section of the joint rotates by about 10’ when loaded, the peel direction no
longer coincides with the global model axes. To obtain the correct values for peel and shear
stress, a local co-ordinate system was used which rotates with the joint. This does not affect
stress invariants such as von Mises stresses.
Variations made to this model are described in the relevant sections.
2.2 BUTT TENSION JOINT
The standard butt joint considered here was:
l
l
Adhere&
Mild steel
Adhesive:
Araldite 2007
l
Diameter:
28mm
l
Adherend length
12.5 mm
l
Adhesive thickness:
0.25 mm
l
Fillet:
none
l
Failure load
45.49 kN (average value for control samples)
For most of the assessments, an axisymmetric model was used. Again second order, reduced
integration elements are used (CAXW). Only half the joint needs to be modelled because of
axial symmetry. There are no geometric non-linearities and the adherend does not yield. Most
of the changes in stress are in a small region at the outside edge of the adhesive, due to Poisson’s
effects, and the grading of the mesh reflects this (Figure 3). Four elements are used through the
(half) thickness of the adhesive at the outside edge, reducing to one element through the
thickness in the middle. To avoid distorted transition elements in the thin layer of the
adhesive, multi-point constraints were used for mesh refinement in this region. A uniform
pressure was applied on the top of the adherend. The mid-plane of the adhesive was
constrained axially to reflect the symmetry.
The modulus of the adherend is about two orders of magnitude greater than the modulus of the
adhesive. Initial runs indicated that the strains of the adherend were very small. This suggested
that the adherend could be modelled with rigid elements instead. This is important because it
4
greatly reduces the size of the model required when investigating non-axisymmetric changes
such as bond angle, which requires a full three-dimensional model. This is described in full in
section 3.3.1.
3. Sensitivity Study
3.1 INTRODUCTION
A large degree of variability occurred in the test results from what were nominally the same
joint and testing conditions. Some of this variation may be due to slightly different procedures
used at the various test centres. The lap shear joints appeared to have greater variation in their
test results than the butt tension joints. The aim of this study was to investigate the causes of
variation in the test results and to try to establish whether the lap joint is inherently more
sensitive to small variations in test conditions than the butt tension joints.
A large number of variables could potentially change the strength of the joint. The preparation
and curing of the adhesive may be different, or the pressure applied during bonding could vary.
Many of these changes cannot be modelled using the finite element method. Changes in test
geometry can be modelled relatively easily, and these effects are investigated here.
3.2 LAP JOINTS
3.2.1 Effect of Gauge Length
The length of the lap joints used in the durability test was 80 mm. The gauge length was 40
mm. This gauge distance was varied in the model by moving the constraints and the position of
the load. The range of lengths considered were from just either side of the lap joint (13 mm) to
nearly the full length of the specimen (70 mm). Figure 4 shows the von Mises stress in the joint
and the displaced shape when the gauge length is 70 mm. Note the high stresses in the
adherend where it bends. Figure 5 shows the corresponding contour plot, to the same scale,
for the joint when the gauge length is 13 mm. In this case the stresses in the adherend are 10%
higher because the bending is increased. Figure 6 shows the distribution of von Mises stress
along the mid-plane of the adhesive for the two joints. The distributions are virtually
indistinguishable.
Figure 7 shows the distribution of interfacial peel stress along the two joints. There are some
minor differences but again they are not significant. Similarly, there is little difference in the
shear stress distribution (Figure 8).
It appears that the gauge length has no real effect on the stress distribution in the lap joints. It is
easily controlled in testing; and the range of values shown here are unlikely to occur in the
laboratory.
3.2.2 Application of Load
The analyses in section 3.2 assumed that the ends of the adhere& could move vertically
relative to each other (when viewing the FE model), so that they lined up after loading. This
reflects the testing situation where universal joints will allow this movement. In some cases the
5
I
ends of the adhere&s have been forced to move parallel to each other, that is no vertical
movement is allowed. One analysis was performed to calculate the effect of this different
arrangement. Although the displacements are quite different (Figure 9), there are no significant
differences in the overall von Mises stress distribution (Figure lo), or in the stress distribution
along the length of the joint (Figure 11). Bending of the adherend occurs further away from
the overlap than previously.
3.2.3 Effect of Bond Angle
A major problem when making lap joints is ensuring that the bond line is even. It is very easy
for the bond to be tapered. For the finite element analysis it was assumed that the centre of the
bond remained at 0.25 mm thick and the angle was varied by lo and 2*,which is shown in
Figure 12. The maximum variation possible using this assumption is 2.9’.
Figure 13 shows the distribution of von Mises stress along the mid-plane of the joint for the
same load and for lower loads on the angled joint. The difference in the peak value is small, but
there is a significant region of the angled joint where the adhesive has become fully plastic (c.f
the stress-strain curve in Figure 2). Using the peak stress as a failure criterion is not very useful
in this case as it masks the true nature of what is occurring within the joint. The failure criteria
would have to take account of the amount of plasticity. If the small plateau for the normal joint
(0’) is treated as a critical crack length, then the angled joint could be considered to have failed
when the plateau in its stress distribution reaches that critical value. Taking this approach does
not give a clear result as the distributions are different but an estimate of the failure load for the
angled joint is 4.5 kN, a reduction of 14%. Looking at the interfacial stresses, again predict the
failure load will be reduced, as can be seen horn the distributions in Figure 14 and Figure 15.
There is a 70% increase in the peak peel stress at the right hand end of the bottom face for the
same load. However , this stress is less than the absolute peak so it is hard to quantify any
difference this might make.
The actual variability in the durability tests was _+7%, a total variation of 14%. These analyses
also showed a total variation of 14% when the bond angle is as much as 2’. Of course a 2’
angle is an extreme case, but clearly the bond angle is quite important to the stress distribution
in the lap joint and is probably the main cause of variability in the results.
3.2.4 Effect of skew
Another possible manufacturing defect in lap joints is that the two adherer& could be skewed
relative to each other. This would add an extra component of shear into the joint when pulled.
To analyse this properly, a three-dimensional model would be required. Observation of actual
lap joints shows that there tends to very little skew due to the use ofjigs during bonding; the
main defect is in the bond angle, therefore no analyses have been done to study this effect.
3.2.5 Effect of Adhesive Modulus
In this section the modulus of the adhesive was varied by 10% above and below normal in the
elastic region. In the non-linear region, for any given strain, the stress was varied by 10% above
and below the normal data.
Figure 16 shows the von Mises stress distributions for the three cases at the same load. Using
the critical length criterion, then for a reduced modulus the failure load will remain the same,
but for the increased modulus, the failure load will increase. If the absolute value of stress was
6
I
used then obviously there would be a HO% difference. In practice, however, any change in
adhesive modulus, due for example to a different cure rate, would also results in a change in
strength. This effect cannot be accounted for in this model without further data.
3.2.6 Yielding of the adherend
The stresses in the lap joint are strongly dependent on the deformed shape, which in turn
depends on the yield point of the adherend. Others have found that the yield point of mild
steel adhere& can vary by as much as 50%. For this sensitivity analysis, the two extremes of
plus or minus 50% were studied, plus some additional points in between. The elastic modulus
was unchanged in all cases. The values used are given in Table 1, and the stress-stain curves are
shown Figure 17. Yielding ofthe adherend does not occur in butt joints.
Table 1 - Adherend yield stress
Fraction of normal yield point.
First yield point (MPa)
Second yield point (MPa)
50%
60%
75%
110
132
165
215
258
323
100%
150%
220
330
430
645
The same failure criterion was used as in section 3.2.3. This gave the set of results shown in
Figure 18, which are the von Mises stress distributions in the adhesive at the failure load. For
the increased adherend yield stress there is little tierence in the failure load or the stress
distribution. For the lower yield stress, the failure load is decreased and the distribution
becomes flatter in the middle. Figure 19 shows that for the worst case (50% yield strength), the
adherend has yielded across the whole width at either end of the joint, thus increasing the angle
of the joint. Any increase in load will produce plastic collapse.
Figure 20 shows the overall effect of adherend yield strength on the failure load. There appears
to be a critical value above which the failure load does not increase. This critical value is
probably related to the adhesive yield strength. For the range of values shown, the maximum
difherence in failure strength is 24%.
3.3 BUTT JOINTS
3.3.1 Effect of Bond Angle
A similar approach was taken as to that used in the assessment of the lap joint. It was assumed
that the centre of the joint remained at 0.25 mm thick and that the joint could be angle about
this point. Using this assumption, the maximum bond angle possible in a 28 mm diameter joint
is 1.0’. This is a third of the angle possible in a butt joint.
The initial model used to study the effect of bond angle was a three-dimensional model as
shown in Figure 21, with a 0.5’ bond angle. First order brick elements with reduced
integration (C3D8R) were used, with two elements through the thickness of the adhesive.
Only a small portion of the adherend was modelled to minimise the model size. Only halfthe
joint was modelled because of symmetry. The mesh density is greatly reduced, and combined
with the use of first order elements, the accuracy of the model will also be reduced.
7
The peel stresses for this model are shown in Figure 22 and compared with the results from the
axisymmetric model. There is little Werence between the two sets of results. The threedimensional model has failed to predict the stress peaks at the outer edge. A 0’ model was not
done in this case for comparison.
The initial axisymmetric analyses showed that the strain in the adhere& was very small, less
than 0.2% axially (Figure 23) and less than 0.1% radially (Figure 24). The corresponding
maximum strains in the adhesive are 2.1% and 1 .l% in the axial and radial directions
respectively. This lead to the idea of using a rigid adherend for the three-dimensional analyses
required for studying the effect of bond angle. The adhesive was modelled as before but the
lower surface was fixed rigid using constraints. The top surface was covered with rigid elements
that keep the surface planar and did not allow any radial or circumferential displacements. The
pressure load was applied to the top surface of the adhesive elements. The cases modelled were
0’ (the mesh is shown in Figure 25), 0.5’, and 0.8’.
The 0’ case agreed very well (-lo/)
o with the axisymmetric model over most of the joint, as
shown in Figure 26. However, it failed to predict the stress peak at the outside edge of the
joint. Figure 27 shows the comparison between the three angled joints. There is less than 1%
difference in the stresses along most of the joint, which is not significant. If the failure is due to
the stress across the whole area of the joint, then there will not be any change in strength. If,
however, the failure is due to the stress peaks at the end then a more detailed model of these
peaks needs to be made. Figure 28 and Figure 29 show the contour plot of peel stress in the
adherend for the 0’ and the 0.8Ojoints respectively. The differences are very small.
A sub-model was created covering the outer 1 mm of the joint and a 5’ arc. This sub-model
had a greatly increased mesh density, with eight elements through the thickness of the adhesive.
Second order brick elements were used (C3D20R) as a further refinement to the model. The
constraints were as before, but the displacements on the outside edges of the sub-model were
interpolated from values given in the full model. This interpolation from 2 first order elements
to 8 second order elements results in the displacements and stresses in the boundary regions
being less accurate. This is illustrated by Figure 30, which shows the displacement of the 0’
submodel. There is a kink right hand comer of the adhesive where the boundary displacements
have been interpolated from the global model. This is the best displaced shape possible with
two first order elements through the thickness. This kink quickly dies away to give a smooth
curve at the front comer. The contour plot of peel stress (Figure 31) appears to show that these
edge effects are limited to one element from the edge and the boundary is sufficiently far from
the area of interest not to affect the stresses there (St Venant’s principle). The results for the
0.5’ submodel are very similar.
Figure 32 shows a graph of the peel stresses at the interface superimposed on the results for the
global model. At the boundary between the global model and the submodel there is quite
some variation, as explained above. From about r-=13.2 mm to r=13.5 mm, the results corn
the global and submodels agree. At the outer boundary, the submodels have predicted the
stress peaks that the global model failed to calculate. However, the value for the 0’ model is
about 13% higher than for the axisymmetric model. The same number of elements has been
used through the adhesive thickness for both models, so this suggests that the submodel analysis
is unreliable. It has also been found that the number of elements used in this region can affect
the magnitude of this peak. A further issue is that the stresses predicted are sufficiently high to
8
cause localised cracking and a redistribution of the stresses. This is an aspect not considered in
the finite element model.
The conclusion from this section is that the angle of the bond line in a butt joint has very little
effect upon its strength.
3.3.2 Applied Bending Moment
A non-zero bond angle inevitably means that the test machine will apply some bending
moment to try to straighten the joint as the load is applied. In the previous analyses, the load
was applied by a uniform pressure on the face of the rigid surface. This does not apply any
bending moment. If, however, the load is applied in the vertical direction to a reference node
for the rigid surface, a bending moment will be induced. The reference node can be moved
relative to the adhesive to simulate different lengths of adherend; the minimum length is 12
mm. This emulates more precisely the loading conditions that would occur in a real test
machine _
Figure 33 (0.8’ butt joint) and Figure 34 show that the introduction of the bending moment
has a significant effect on the peel stress in the adhesive. There is a 10.3% increase in the peel
stress compared with the angled joint with no bending moment. Obviously this will have a
great effect on the strength of the joint. The variation is almost as much as in the angled lap
joint. In this case the load is applied 12 mm above the top surface of the adhesive. Depending
on the design of the testing machine, the specimen design and the test procedure, the bending
moment applied could be much greater.
3.4 CONCLUSIONS
The purpose of the sensitivity study was to show how variations in joint preparation could
affect the results of the durability tests, and in particular to show why the lap joint is more
sensitive to initial variations than the butt joint.
The first variation examined was the gauge length of the lap joints. Analysis of the extremes of
gauge length showed that there was very little effect on the overall stress distribution within the
adhesive. There were some minor changes at the end when the gauge length was very small.
In reality the actual gauge length is not going to vary as much as studied here, so the conclusion
from this section is that there is no effect. As a subset of this section, two ways of loading the
joint were examined. The first assumed that the test machine had universal joints so that the
ends of the adherend tend to line up with each other at the end of the test. The second is
where the ends of the adhere& are forced to remain parallel so that they do not line up at the
end of the test. The analyses showed that although the displacements of the adhere& were
quite different, there were no significant differences in the adhesive stress distributions.
The next variation investigated was the angle of the bond line in the joints. Of course these
should be nominally O”, but examination of some joints shows some considerable variation in
this angle. For a 2’ angle, the reduction in strength could be as much as 14%. The variation
found in the durability tests was also 14%.
Another possible manufacturing defect is skew of the two adherends, although this has not been
observed to occur to any great extent in real joints as jigs are used to ensure minimal variation.
9
This would lead to an additional shear component in the adhesive as the adhere& are
straightened out during the test, resulting in a reduction in strength.
No firm conclusions can be made about the effect of the adhesive modulus on the joint
strength, because any ditferences in cure procedure that would produce a change in modulus
would also change the strength of the adhesive and strain to failure. Also, there may be changes
in the interfacial strength for which no data was available. In general, however, a like for like
reduction in strength was obtained for a reduction in modulus Xall other parameters remained
constant.
The variation in adherend yield strength had a large effect on the strength of the joint. It has
been found that the adherend yield strength can vary by as much as 50%, although this depends
on the thickness of the adherend specimen. As the final yield strength is reduced, more rotation
occurs in the joint and the joint fails at a lower load. The critical parameter is the ratio of
adhesive to adherend yield strength. For wet joints this is decreased so that failure is much
more likely to occur in the adhesive than in the adherend.
For the butt joint there is much less scope for variation. The adherend does not yield, so there
is no point in varying the yield strength. As the peel strength distribution is almost uniform,
then any changes to the adhesive modulus will follow a one-to-one relationship. This only
leaves the variation of the bond line angle. A significant point is that the angle can only vary by
lo in the butt joint (assuming constant average bond thickness) compared with almost 3’ for the
lap joint, so there is less scope for variation. The analyses have shown that even taking an
extreme angle of 0.8’ has very little effect on the stress distribution in the joint.
The additional bending moment that may be applied by the testing machine ifthe joint is
angled does, however, have a significant effect on the stress distribution. The decrease in failure
stress could be as much as lo%, although this remains less than is possible with a lap joint.
The overall conclusion is that the lap joint is far more sensitive to variations in geometry and
material properties than the butt joint. Indeed there are more ways to vary the geometry of the
lap joint compared with the butt and the effects of these variations are cumulative.
Experimental experience has shown that there is a greater variation in lap joint test results
compared with butt joints, a feature that is born out by the finite element analysis. These
analyses have been largely qualitative, as to put a quantitative figure on the variation that could
be expected in practice would need complex statistical analysis of the various parameters.
10
4. Durability
4.1 INTRODUCTION
This section describes a series of finite element analyses performed to investigate the long term
durability of lap and butt joints. A semi-empirical approach was taken using the results from
the durability tests carried out as part of task 2l along with bulk adhesive test data which were
then combined in a finite element model. The result is not intended to be a general predictive
model rather a methodology that could be applied to a particular adhesive, adherend, and
surface preparation combination.
4.2 ADHESIVE
Two bulk samples of adhesive were immersed in water at 60°C for several weeks until they
were saturated. The samples were approximately 60~1OXl mm. They were tested in tension
by AEA Technology immediately after being removed from the water. Several dry specimens
from the same batch were also tested. The results are shown in Figure 2. There has been a
reduction in both the elastic modulus and the yield stress for the wet adhesive. The final yield
stress for the saturated adhesive is about half that of the dry adhesive. The strain to failure of the
wet adhesive is, however, less than that for the dry, which is contrary to normal expectations.
Data obtained later fi-om Oxford Brookes University’ (OBU) suggests that the strain to failure
of the wet adhesive is double that for the dry adhesive. There is fairly good correlation
between the two sets of results for dry 2007, and in the elastic region for the saturated samples.
Dog bone test pieces were used for the OBU tests rather than the rectangular pieces used by
AEA Technology.
Adhesive data was also taken horn a number of other sources. For the dry adhesive, tests
carried out as part of MTS Project l4 show good agreement with the data used here. There is
also a variation in the shear properties of the adhesive 5 with water content which does not
follow the isotropic relationship of G=E/2(1 +v). These values of shear modulus were
measured from thick adherend shear tests (TAST), and typical results are show in Figure 35.
A difision coefficient of 6.4~10-‘~ m2/s was obtained from bulk adhesive tests6, however,
measurements of weight gain in lap joints7 predict a much higher diffusion coefficient of
6.7~10~‘~ m2/s using a 1 mm thick grit blasted stainless steel adherend. The value changed with
a different adherend which indicates that inter-facial effects have an influence on the diffusion
rate. Unfortunately, diffusion measurements were not made on silane treated steel adhere&.
Measurements using dielectric sensors embedded within the joint compared well with
calculations assuming the bulk adhesive diffusion coefficient and Fickian behaviour. However,
measurements of the dielectric constant taken across the adhere& showed a much higher
degree of water uptake, indicating that there is a significant difference in water concentration
across the thickness of the glue line. To avoid the problem of which dif&sion coefficient to use
in the finite element model, a non-dimensional parameter tD/A was used instead of time,
where t is time, D is the diffusion coefficient and A is the area of the joint. A diffusion
coefficient would have to be assumed for the test results so that they could be plotted on the
11
same scale. This value could reasonably be varied between the bulk and joint diffusion
coefficients to produce a better fit ifnecessary.
Another potentially significant factor in the strength of the joints is swelling of the adhesive.
This will introduce a compressive stress in regions of high water content. Data for the swelling
of 2007 has been measured as part of task 5’ and is shown in Figure 36.
4.3 FINITE ELEMENT MODEL
The model used was largely the same as for section 3, but with several differences made to the
material model. Incorporating the variation in shear modulus with water content in the finite
element model required the use of general orthotropic properties. This excluded the use of
non-linear properties. Most of the subsequent analyses have therefore used linear-elastic
properties.
The dif&sion of water into the joints was modelled using a transient heat transfer analysis, as the
governing equations of Fickian diffusion and heat conduction are identical. The resulting
temperature distribution was then entered into the structural analysis, where the material
properties were dependent on temperature rather than ivater concentration. For the butt joint,
a temperature of 10°C was applied to the outside edge (to correspond to a water concentration
of 10%) and the analysis run through several time steps, corresponding to the testing times.
The diffusion model in the lap joint is slightly more complicated. Previous analyses of the lap
joint in this study have used two dimensional elements. If this model was used for the di&sion
calculation, then this would be equivalent to diffusion from two edges, as shown in Figure 37a.
However, in reality difhzsion would occur from all four edges as shown in Figure 37b. This
will have two effects. The first is that saturation of the joint will occur much more quickly.
The second is that at intermediate times there will be swelling at the edges, but this would
require a full three dimensional model to analyse this effect. With either case, saturation occurs
before 60 weeks using the high di&s ion coefficient, so that the two dimensional model could
be used for the saturated case. For the sake of simplicity, the two dimensional model has been
used throughout.
Just performing the d&Fusion analysis with water entering &om all four sides (Figure 38) shows
an interesting correlation with the halo effect reported in reference 1. Using the high d&sion
rate, full saturation is achieved afier 12 weeks, and the halo seen in the lap joints completely
covers the area of the joint at this time.
4.4 RESULTS
4.4.1 Butt Joints
The analysis of the butt joint with adhesive properties varying in accordance with moisture
content, but without adhesive swelling, shows a decrease in the stress at the outside edge of the
joint with time for a given load. ,There is a corresponding increase in the stress at the centre of
the joint, as shown in the sequence of stress distributions in Figure 39. With swelling included
this effect is much more pronounced, as shown by the sequence of graphs in Figure 40.
When studying dry joints, a failure criterion based on the average stress is possible because the
stress distribution is almost uniform. However, for the wet joints the stress distribution is no
12
longer uniform so some other criterion needs to be used. A criterion based on the stress
singularity at the outside edge would not be useful either as it does not really take account of
what is happening in the majority of the joint, and its value is determined by the number of
elements used in the analysis. A point stress criterion ignoring the singularity and taking into
account the reduction strength of the adhesive with water content would be more appropriate.
A possible failure criterion can be based on the strengths of the butt joint when dry and when
fully saturated. The failure strength can be defined as Equation 1
where
C
Cmax
Ofti
Odry
0wet
water concentration (%)
saturation water concentration (%)
adhesive tensile failure stress at water concentration C
adhesive tensile failure stress when dry
adhesive tensile failure stress when saturated
Using this equation, the failure stress at each point in the joint was plotted against the stress
distribution obtained from the finite element analysis. The stresses were then scaled (as linearelastic properties were used, although swelling adds some non-linearity) so that the two curves
just touched to find the failure load. The dry strength was found from the week 0 test results
and peak stress from the finite element analysis (but not the singularity stress). For the wet
adhesive strength, the load at week 60 (for the high diffusion rate) was set to the failure load as
measured in the durability test, and the value of o,, was adjusted until the failure criterion was
satisfied. Two separate values of o,,, are needed for the two different surface treatments used
in the tests. In both cases the effects of swelling were incorporated into the finite element
analysis. These gave the values of odry and o,,, as shown in Table 2.
Table 2 - Adhesive failure stresses MPa
~~
Using this criterion (which shall be called the peel failure criterion) produced the strength
retention curves shown in Figure 41. For the grit blast case, this criterion produces an almost
perfect match. However, for the grit blast and silane case there is poor correlation, except at
the ends where the results are identical by definition.
Another criterion (which will be called the dry-wet criterion) used a single value of wet
strength, taken from the results at 36 weeks, at all times other than for week 0. This is justified
for interfacial failure because the diffusion rate in the interface is much higher than in the rest of
the adhesive, so it is reasonable to expect the interfacial strength to drop rapidly to some
asymptotic value. Of course, this is an over-simplification and there may be some errors in the
results at the earlier times. For the grit blast case this produces a strength retention curve which
is shown in Figure 42. After some iteration (and also considering the lap joint results in section
13
4.4.2), the best fit was obtained by using a diffusion coefficient of 8.Ox1O-‘3 m2/s (Figure 42).
This is slightly higher than the measured bulk diffusion coefficient, which will be governing the
plasticization and the swelling. Water from the interface will seep into the bulk adhesive giving
a higher apparent diffusion coefficient.
Once again the results for the girt blast and silane case did not fit very well, regardless of the
diffusion coefficient used.
4.4.2 Lap Joints
4.4.2.1 Introduction
The test results for the lap joints exhibit a complex behaviour. There is an initial drop in
strength after 3 weeks, followed by an increase at 6 weeks (Figure 44). After this time there is a
gradual decay in strength back to its original level. This characteristic dip and recovery in
strength was echoed at two different laboratories confirming that the results are genuine,
although other adhesive do not exhibit this behaviour to this extreme. The butt joint does not
show this behaviour, suggesting that the failure mechanisms in the lap and butt joints are
different. At the last time tested, 36 weeks, the butt joint is not fully saturated, whereas the lap
joint is saturated after 12 weeks because of its smaller area.
MTS Project 2 has considered failure criteria for adhesive joints in some detail’ but with limited
success for lap joints. A point stress criterion was found to work for a limited range of dry lap
joints”, h owever, it would be difficult to apply such a criterion to wet lap joints because of the
additional complexity of varying material properties with water content and swelling. Any
such physical point used for the criterion would be likely to move with the ingress of water.
4.4.2.2 Linear Analysis
Figure 45 shows a sequence of stress distributions for lap joints without swelling and with the
high diffusion coefficient (4.9~10-‘~rn~/s). The same load has been used for all the cases. After
three weeks, there is a 20% reduction in the peak peel stress (ignoring the singularity at the left
hand side of the graph). Th’1s is due to plasticization of the adhesive. After this time, the peak
peel stress stays constant. Figure 46 shows the equivalent sequence including swelling effects.
After three weeks the peak peel stress has not reduced as much as in the joint without swelling.
There are now regions of tension at 2.5 mm horn each end of the joint. This is more
significant for the analyses using the low diffusion rate. The peak peel stress then increases
slightly for weeks 12 and 60. The final value is higher than for the case without swelling. The
benefit of the reduction in stress will be countered by the decrease in strength of the adhesive
adherend interface.
The peel stress criterion used for the butt joints was also applied to the lap joints. The adhesive
strengths obtained &om the butt joint analyses were used, and the criterion was applied to the
peel stress in the lap joints. Using this criterion produced an initial increase in the strength to
126% (Figure 47) of the dry strength followed by a rapid decrease to 61% of the dry strength.
There is then a very slight recovery before the strength remains constant at 63%. The final
failure load is 20% lower than the test results.
A modified version of this criterion was proposed in which the von Mises stress was compared
against the failure stress predicted by Equation 1. As the stress distribution is biaxial rather than
uniaxial, as in the butt joint, this should be a better criterion. For the grit blast case there is no
initial rise as for the other criteria, but a rapid fall to 50% of the dry strength. After this the
14
strength remains almost constant. This clearly does not correlate with the test results. Using
the strengths from the grit blast and silane butt joints, the initial fall is to 75% and then there is
some recovery to 78%. This criterion does not predict the significant recovery in strength that
is shown by the test samples.
The best fit obtained using the dry-wet failure criterion, using a diffusion rate of 8.Ox1O-‘3
m2/s, for the grit blast case. Initially there is a 40% rise in strength (Figure 48), which is the
opposite to the test results, but after that the results correlate quite well. The case without
swelling is also shown in this graph. This matches the initial response well, but does not show
any recovery in strength. This suggests that the amount of swelling may be over estimated,
which would affect the initial response, or that the criterion needs to be modified, for example
to take into account of how much of the joint is in tension or compression. As stated earlier,
more of the joint is in tension at the earlier times even though the peak stresses are lower.
The results of the analyses were compared to one of the variant tests performed (a 10x10 mm
lap joint instead of 20x10 mm). Apart from the result at week 3, there is good correlation
(Figure 49) with the test results in both the magnitude and the shape of the strength retention
curve. This time however, the no swelling case does not match the initial drop.
As with the butt joints, the results for the grit blast and silane case did not correlate very well
with the test results (Figure 50). With swelling included, the values are too high and the shape
of the curve is not very good. Without swelling, the strength of the joints has increased because
the stresses have reduced, but the adhesive strength has apparently remained constant (from the
butt joint results). It is possible that the improved surface treatment has made interfacial failure
less likely. The criteria considered so far assume that failure is interfacial. The introduction of
silane primer is aimed principally at improving the inter-facial properties so that the failure mode
is more cohesive.
4.4.2.3 Non-linear analysis
As has already been noted the stress-strain curve for 2007 is highly non-linear and this may be
why the previous analyses have been unable to predict the strength retention in the lap joints.
In this section the non-linear properties of the adhesive, as measured by 0BU3, have been used.
The use of non-linear properties meant that the variation of shear modulus with water content
could not be accommodated in this model.
The failure criterion used for these analyses was that failure occurred when the load increment
required by the finite element analysis went below l~lO_’ of the load applied. This is
effectively where there is a “knee” in the force-displacement curve at the point where the load
is applied, after which the displacements increase to infinity without any further sign&cant
increase in load. This is the maximum load theoretically possible. This occurs when the entire
adhesive layer has yielded. This “limit state stress” criterion was suggested by Crocombe” but
as it applies only to adhesives with a high ductility, it is then reasonable to assume that this is the
case for the wet adhesive, but not for the dry adhesive. Therefore this analysis can only really
be justified for a full saturated joint. This method inherently provides an upper bound value as
mechanisms such as fracture could reduce the ultimate failure load.
Using this method produces the strength retention curve shown in Figure 5 1. The initial
strength prediction when dry is too high. This was expected as the dry adhesive is relatively
15
i
brittle. For the later times, the curve is in between the test results. It was expected that the
curve would lie above the test results as it should be an upper bound. The material data
measured could be wrong because the adhesive may have been prepared in a different way to
the durability tests.
4.5 DISCUSSION
4.5.1 Butt joints
The failure criteria were all fitted to the butt joint results at 0 and 36 weeks. Both the peel
failure criterion and the dry-wet criterion could be fitted to the grit blast strength curve at all
times by varying the diffusion coefficient. The further correlation with lap joints using the drywet criterion suggests that this method could prove useful in the prediction of the long term
performance of adhesive joints. Neither of the criteria correlated with the grit blast and silane
case very well. More test data after longer periods of immersion is required to determine
whether the strength continues to fall or reaches an asymptote as for the grit blast case.
4.5.2 Lap joints
None of the criteria used correlated with the test results at all times. It appears that the effect of
swelling, as modelled, has suppressed the stresses too much at week 3 resulting in an artificially
high strength at this time. This effect is not apparent when using the von Mises criteria, the
non-linear analyses, or when there is no swelling. The non-linear analyses produce a dry
strength that is too high. This is probably because the limit state criterion used only applies to
ductile adhesives; the dry adhesive is not particularly ductile and a brittle fracture type failure is
more common. Some other criterion would have to be used for the dry case where brittle
fracture is more likely to occur.
It appears that there are different rates for various mechanisms. For swelling and plasticization,
the bulk adhesive diffusion rate would be the most appropriate, but for the reduction in
strength, which is likely to take place at the interface, the high diaision rate, as measured in
actual joints, would be more appropriate. Not enough information is currently available to
model the interface (or “interphase”) accurately.
4.6 CONCLUSIONS
The failure criteria used here have been empirical in nature by fitting the results for the butt
joints, and then using the same data to attempt to predict the strength of the lap joints. This has
been partially successful, but none of the criteria used matched the results at all times. The most
likely reason is that two different failure criteria have to be used at difherent times. When the
adhesive is dry (say up to 3 weeks) then a fracture mechanics criterion would be appropriate.
At later times as the water uptake increases, the adhesive will become more ductile so a
different criterion would be required, for example the dry-wet failure criterion used with some
success in this study or a non-linear “limit state stress” criterion which has also been shown to
give a good correlation at later times. This double failure criteria approach is illustrated in
Figure 52.
There is a strong argument for having two difKtsion rates, a high difhtsion rate for weakening of
the interface and a low diffusion rate (based on the bulk adhesive tests) for the plasticization and
swelling. This supported by evidence gained from the difhtsion measurements taken and the
partial correlation of the dry-wet criterion with the test results.
16
To make further progress with this approach, all of the material properties need to be measured
carefully, including those of the adherend which, as shown in section 3.2.6, can affect the
results. Care should be taken that the adhesive is prepared in the exactly the same manner as for
the joints.
5. Acknowledgements
This report is based on work carried out under a DTI funded Measurement Technology and
Standards (MTS) programme on the performance of adhesive joints.
The authors would like to thank Richard Lee and Terry Yates of AEA Technology who
carried out the bulk adhesive tests for the work in this report.
17
3
7. Table of figures
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22
Figure 23
Figure 24
Figure 25
Figure 26
Figure 27
Figure 28
Figure 29
Figure 30
Figure 31
Figure 32
Figure 33
Figure 34
Figure 35
Figure 36
Figure 37
Figure 38
Figure 39
Figure 40
Mesh of lap joint
Stress-strain curve for Araldite 2007
Mesh of butt joint
Mises stress in lap joint with gauge length of 70 mm
Mises stress in lap joint with gauge length of 13 mm
Mid-plane von Mises stress for lap joints with gauge lengths of
13 and 40 mm
Interfacial peel stress for lap joints with gauge lengths of 13
and 70 mm
Interfacial shear stress for lap joints with gauge lengths of 13
and 70 mm
Displacements of lap joints with normal and parallel loading
Mises stress in lap joint with parallel loading
Mid-plane von Mises stress for normal and parallel loading
Mesh of angled lap joint
Mid-plane von Mises stress in angled joints
Interfacial peel stress in angled joints (top face)
Interfacial peel stress in angled joints (bottom face)
Effect of adhesive modulus on lap joints
Adherend stress-strain curve.
Mises stress in adhesive at failure .
Mises stress in lap joint with decreased adherend yield stress at
failure.
Effect of adherend yield stress on failure load.
Mesh of 3D butt joint full model.
Peel stresses in butt joint.
Axial strain in axisymmetric butt joint model.
Radial strain in axisymmetric butt joint model.
Mesh of rigid adherend model for 0’.
Interfacial peel stress in 0’ butt joint.
Interfacial peel stress in angled butt joints.
Peel stress in adhesive in 0’ butt joint.
Peel stress in adhesive in 0.8’ butt joint.
Displacement of 0’ submodel.
Peel stress in 0’ submodel.
Interfacial peel stress in submodels.
Mises stress in 0.8’ butt joint with bending moment applied.
Effect of bending moment on butt joints.
TAST Results.
Swelling of Araldite 2007.
Diffusion into lap joints.
Diffusion from all four sides.
Peel stress and water distributions in butt joint without swelling
Peel stress and water distributions in butt joint with swelling
19
I
Figure 41
Figure 42
Figure 43
Figure 44
Figure 45
Figure 46
Figure 47
Figure 48
Figure 49
Figure 50
Figure 51
Figure 52
Butt joint strength using peel failure criterion.
Butt joint strength using dry-wet criterion (grit blast)
Butt joint strength using dry-wet criterion (grit blast and silane)
Test results for lap joints
Peel stress and water distributions for lap joints without swelling
Peel stress and water distributions for lap joints with swelling
Lap joint strength retention (grit blast - peel failure criterion)
Lap joint strength (20x10 mm - grit blast - dry-wet failure
criterion)
Lap joint strength (10x10 mm - grit blast - dry-wet failure
criterion)
Lap joint strength (grit blast and silane - dry-wet failure
criterion)
Lap joint strength - non-linear analysis
Failure modes
20